Digitally controlled oscillators (“DCOs”) are used in a variety of integrated circuit applications. A critical performance parameter of a DCO is the frequency of its oscillating output signal. Some integrated circuit applications may require the oscillator frequency to be adjustable. In some applications, the oscillating frequency of a DCO may be based on the resonant frequency of an inductor-capacitor resonator (“LC-resonator”). In such applications, the oscillating frequency of the DCO may be adjusted by varying the capacitance in the LC-resonator. However, the tuning resolution of the frequency may be limited by the minimum step size of the variable capacitor. Moreover, a single fixed step size for the variable capacitor may result in different frequency tuning step sizes at different DCO frequency ranges.